An Algebraic System and Its Application
Received:September 15, 2005  Revised:July 16, 2006
Key Words: algebraic system   Volterra lattice hierarchy   integrable coupling system.  
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Author NameAffiliation
WEI Yuan Department of Mathematics and Information, Binzhou University, Shandong 256600, China 
ZHANG Yu-feng School of Information Science and Engineering, Shandong University of Science and Technology, Shandong 266510, China 
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      An algebraic system $X$ is constructed by using the known loop $\widetilde{A}_{1}$. Then a new isospectral problem is established by taking advantage of $X$, which is devoted to working out the well-known Volterra lattice hierarchy. And an extended algebraic system $\widetilde{X}$ of $X$ is presented, from which the integrable coupling systems of the Volterra lattice is obtained.
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